The disposable income of residents can reflect the living standard of people in the area. For government departments, it is necessary to master the trend of rural resident income to formulate corresponding policies benefiting farmers. Thus, this paper proposes a grey model with an improved jellyfish search optimizer to predict the rural resident income in Shaanxi Province. Firstly, by applying fractional-order modified strategy and Gaussian mutation mechanism to the original algorithm, the proposed algorithm shows better performance in solving accuracy, stability, and convergence acceleration when compared with different classical methods on cec2017 and cec2019 test functions. Then, based on the fractional time-delayed grey model, a discrete fractional time-delayed grey model with triangular residual correction (TDFTDGM) is proposed by replacing the derivative with a first-order difference and introducing the triangular residual correction functions. Finally, the improved jellyfish search optimizer is used to explore the optimal order of the TDFTDGM model. The all-around performance of the forecast model is incomparable to additional grey models compared on four measure criteria, which means it is a practical approach for long-term prediction with small samples. Moreover, the forecast data of rural resident income in Shaanxi Province from 2021 to 2025 are given for reference.

Carbon emissions, as an indicator of green economic development in urban agglomerations, are closely related to the degree of coordinated development between cities. Additionally, urban agglomerations, as a highly developed form of urban space, are widely regarded as a more efficient, energy-saving, and land-saving urbanization method. This article constructs an urban agglomeration network based on relevant data from listed companies in the Yangtze River Delta urban agglomeration with practical connections between cities and uses social network analysis methods and a fixed effects model to calculate the impact of overall and individual network indicators of urban agglomerations on urban carbon emissions and collaborative emission reduction of urban agglomerations. The regression results indicate that the centrality of individual cities has a significant negative correlation with the intensity of urban carbon emissions, with a coefficient of −0.067. The centrality of core cities has a significant positive impact on the collaborative emission reduction of urban agglomerations, with a coefficient of 0.0138. The impact of network density on the collaborative emission reduction of urban agglomerations shows an inverted U-shaped curve. Based on the analysis results, the paper explores the spatial structure construction method and industrial development control strategy based on urban agglomeration collaborative emission reduction.